1. What is a Mixed Number Ratio?

A mixed number ratio compares two mixed numbers by finding their greatest common divisor (GCD) and simplifying both numbers by dividing them by this GCD. This creates the simplest whole number ratio between the two quantities.

2. How Does the Calculator Work?

The calculator uses the following process:

Where:

• \( mixed1 \) — First mixed number
• \( mixed2 \) — Second mixed number
• \( gcd \) — Greatest Common Divisor of both numbers

Explanation: The calculator first finds the GCD of both numbers, then divides each number by the GCD to simplify the ratio to its smallest whole number terms.

3. Importance of Ratio Simplification

Details: Simplified ratios are easier to understand and work with in mathematical problems, recipes, scaling diagrams, and other proportional relationships.

4. Using the Calculator

Tips: Enter two positive mixed numbers. The calculator will show the simplified ratio and step-by-step solution showing how the GCD was found and applied.

5. Frequently Asked Questions (FAQ)

Q1: What if my numbers are already in simplest ratio?
A: The calculator will return the same numbers with a GCD of 1.

Q2: Can I use decimal numbers?
A: Yes, the calculator works with both whole numbers and decimals.

Q3: What's the maximum number size this can handle?
A: The calculator can handle very large numbers, limited only by PHP's float precision.

Q4: How is the GCD calculated?
A: Using the Euclidean algorithm, an efficient method for finding GCD.

Q5: Can this be used for more than two numbers?
A: This version is designed for two numbers only, but the concept can be extended.